This project helps investigators to find numerical solutions to complex equations that model biological systems as well as develop mathematical models for such systems. Typical projects this year have included : 1) HIV in vitro kinetics (with J. Spouge, D. Dimitrov, G. Englund). A model has been developed and tested to explain oscillating population sizes in simple infection experiments. The model fits the data without assuming multiple populations of T cells. 2). Hemoglobins (with K.D. Vandegriff, R.M. Winslow, V.W. McDonald, M. Chavez). Oxygenation and oxidation of hemoglobins are studied by spectrophotometry and singular value decomposition (SVD). A study is under way that avoids difficulties inherent in the assumption of the dimerization of tetrameric hemoglobin. 3). Kinetics of Bacteriorhodopsin (with R.W. Hendler, S. Bose). A review of models of light-intensity-dependent kinetics has been published. 4). Kinetics of cytochrome aa3 (with R.W. Hendler, S. Bose). A paper describing a novel mechanism for passing electrons to oxygen has been submitted. 5). Protein-ligand binding (with P.J. Munson, G.E. Rovati). A paper describing a program for nonlinear least squares fitting of binding data is being written. 6). Maximum entropy curve fitting (with H. Fales). The capabilities of an extensive but very expensive program ($15,000 a copy) for fitting peaks to spectroscopic data has been initiated. 7). Thermal transitions in proteins (with J. Ferretti). Conformational changes in protein structure are being studied by circular dichroism and SVD. 8). Electrophoresis in a spatially periodic electric field (with Y. Chen). Material flow is being simulated by differential equations with boundary conditions using sparse matrix methods.